Abstract. The fundamental problem of mechanics is to study
Hamiltonian systems that are small perturbations of integrable
systems. But also perturbations that destroy the Hamiltonian
character are important, be it to study the effect of a small
amount of friction, or to further the theory of dissipative
systems themselves which surprisingly often revolves around
certain well-chosen Hamiltonian systems. Furthermore there are
approaches like KAM theory that historically were first applied
to Hamiltonian systems. Typically perturbation theory explains
only part of the dynamics, and in the resulting `gaps' the
orderly unperturbed motion is replaced by random or chaotic
motion.